Mathematical solutions for two possible pharmacodynamic interactions (linear nonsaturable and nonlinear saturable) between antibiotics and microorganisms derived from the incorporation of clinically relevant antibiotic dosage regimens such as single bolus dosing, multiple doses, and constant infusion at steady state have been obtained. It is concluded that the saturable nonlinear interaction model between the tested antibiotic and microorganism appears appropriate. The model and its derived equations are capable of describing in vivo bacterial growth of P. aeruginosa after single bolus dosing and multiple doses of piperacillin as described by a linear one-compartment pharmacokinetic model. The activity of piperacillin against P. aeruginosa in the neutropenic mouse systemic infection model can be described by an equation with three dynamic parameters: the bacterial growth rate constant kapp, 0.02345 min-1, the bacterial killing rate constant k'kill, 0.02623 min-1, and the Michaelis-Menten type saturation constant Km, 0.05467 microgram/ml. The concept and derived equations for the optimal dosing interval and minimum critical concentration are of clinical importance for the proper selection of antibiotic dosage regimens.